lesson 2

Paramvir Singh
LESSON PLAN 2
Mathematics

EDCP 342A
Date : December 12, 2017    

Room       1213

Topic/learning objectives:  In order to make the aesthetic connection, students will learn about the relationship of arithmetic sequences and geometric sequences with arts. After completing this lecture they would be able to find these artistic mathematical dimensions in nature and in their surroundings.


Resources:

https://en.wikipedia.org/wiki/Sequential_art

https://en.wikipedia.org/wiki/Fibonacci_number
https://books.google.ca/books?isbn=0393346846

archive.bridgesmathart.org/2012/bridges2012-357.pdf

Textbook Pre-Calculus 11





HOOK
  Do you know mathematics has a relationship with arts?
Have you ever seen mathematical patterns in your surrounding?
Have you ever noticed mathematics in designs, drawing, caricature or in writing?
Today we will talk about the beauty of sequences and patterns. Especially we will try to find these artistic patterns in our real -world applications


Lesson content/activities:
 Art represents beauty and aesthetics. In arithmetic progression, there is also a beautiful sequence. The Fibonacci Sequence, has its different kind of beauty which is related with its position of terms and ratio of one number to the next. Each number is the sum of the previous two numbers i.e 0,1,1,2,5,8,13,21,34,55…………
The ratio of one number to the next is 1.61803. It is known as “phi” which is called golden ratio. This sequence has aesthetically beautiful patterns. Even in nature sunflowers represent radical symmetry and numerical symmetry which represent Fibonacci sequence. The spirals in sunflower adds up to Fibonacci number.


This is Fibonacci spiral which is created by drawing circular arcs connecting the opposite corners of squares of sizes 1,1,2,3,5,8,13 and 21



             
Many type of sequences can be found in nature. Even Fibonacci sequence, frequently
found in flowers, seeds and trees. A geometric sequence can be found by the orb web of the common garden spider. It is an impressive architectural feat.    
Similarly, the beauty of mathematics in arithmetic series can be seen in the arrangement of bowling pins and snooker balls. These are arranged in triangular formation. A triangular number is a number that can be represented by a triangular array. Each triangular number is an arithmetic series. The sequence would be 1, (1+2), (1+2+3), ( 1+2+3+4), ( 1+2+3+4+5)……….
The first five triangular numbers are 1,3,6,10,15
Further it can be extended to the general formula for the sum of an arithmetic series to show that nth triangular number is n (n+1) ÷2

Time

10 minutes








50 minutes


Homework/assessment

The teacher will ask them to find these artistic patterns in the real world. They can find such types of sequences in sunflower, snowflakes and shells.



Learning outcomes

All pupils will listen carefully and they will get knowledge of artistic dimensions of sequences and series
Most pupils should understand the beauty of Fibonacci sequence and triangular numbers
Some pupils may try to find this kind of patterns in their surroundings.





Comments/evaluation


Teacher will ask general questions about the relationship of math with arts . It will help him to know about the understanding of topic discussed in the class


Comments

  1. Susan Gerofsky3 January 2018 at 11:34

    Lesson #2: Once again, this is not an adequate lesson plan, for very similar reasons to Lesson 1. Although you have chosen an interesting topic (and one not listed in your list of lessons for the unit, by the way), this lesson plan has many problems:

    • Just a (way-too-brief) teacher script, with no consideration of students' active learning and participation
    •Timings are entirely vague and unrealistic, and don't add up to the length of a typical block
    •'Teacher telling' is not equivalent to good teaching, and students listening to the teacher talk is not equivalent to actually learning mathematics
    •A potentially interesting topic has been squandered by turning it into nothing but teacher talk, where it should be the springboard for active engagement by students with teacher guidance.

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